Hollow Topology Optimization Design For Geometrically Nonlinear Structures

Hollow structures are widely found in both natural and industrial fields.They not only exhibit excellent mechanical properties such as high stiffness-to-mass ratio,but also possess good processability that easily meets the requirements of structural uniformity during the manufacturing process.However,there is currently a lack of effective methods to design hollow structures.Topology optimization,as an efficient design tool,can generate highperformance structures.The corresponding optimized results are usually solid structures that are difficult to be converted directly into hollow structures.Additionally,hollow structures are prone to large deformation,then it is of significance to study the hollow topology optimization design for geometrically nonlinear structures.Therefore,the specific research works in this dissertation are described as follows:In Section 2,the explicit topology optimization method for three-dimensional(3D)structures is proposed by extending the two-dimensional solid moving morphable bars to 3D solid bars.The 3D solid moving morphable bars are projected onto fixed discrete elements,and the corresponding distance functions are constructed and improved.The smooth Heaviside approximation function with the distance function is used to establish the element density function.Additionally,the solid topology optimization model is established under the linear elasticity assumption,and the sensitivity analysis is derived.Then the program codes are provided for the subsequent expansion.The influence of two distance functions on the computational efficiency is compared for the optimization process and the effectiveness of the method is confirmed by the classical cantilever example.In Section 3,the hollow structural topology optimization method is proposed under the linear elasticity assumption.Based on the explicit geometrical description of the 3D solid moving morphable bars,the 3D hollow moving morphable bar is obtained by the Boolean subtraction operation of two solid bars,so the element density function with respect to the hollow bars is easily established.Then,the hollow topology optimization model with minimum structural compliance by volume constraint is established under the linear elasticity assumption.The model not only keeps the advantages of the classical baseddensity topology optimization method to easily calculate the sensitivities,but also can directly obtain the hollow optimized result by controlling the structural geometrical parameters explicitly.In Section 4,the geometrically nonlinear topology optimization method is proposed for the hollow structures.Under the large deformation assumption,the above element density function is used to derive the geometrically nonlinear finite element analysis for 3D structure.Then the corresponding topology optimization model is established,and the adjoint method is used to derive the corresponding sensitivities.Numerical examples demonstrate that the shape of the geometrically nonlinear optimized result is significantly different from the linear optimized result to resist the larger deformation.Furthermore,for structures subjected to bending or torsional loadings,the hollow cross sections of the optimized results exhibit the shapes that facilitate the resistance to large deformation.In Section 5,the multiscale concurrent topology optimization method is proposed for the geometrically nonlinear hollow structure.The macro-element density function is constructed by the 3D hollow moving morphable bars,which are projected onto the lattice cells.The energy-based homogenization method is further modified by deriving the microelement density with solid moving morphable bars.Then the lattice cell is determined explicitly,which is incorporated into the 3D geometrically nonlinear finite element analysis.Afterwards,the multiscale concurrent topology optimization model is constructed by considering the geometrical nonlinearity.Additionally,the modified energy-based homogenization method can be effectively demonstrated for the design of explicit lattice cells,and the validity of the proposed method is confirmed to obtain the explicit multiscale hollow result with lattice cells.Finally,the dissertation extracts the innovation points and makes the prospects.